2026-02-02
Both were commonly represented by probability distribution.
Differ conceptually1:
Variability:
Uncertainty:
Assumption: changes in OFVs (dOFVs) with different parameter values follow a chi-square distribution.
To obtain CI of a parameter (e.g., \(\theta_1\)):
Fix value of \(\theta_1\) other than its final estimate while keep all other parameter unfixed.
Refit the model to obtain the OFV.
Find values of \(\theta_1\) that changes OFV by, for example, 3.84 (P value=0.05 with df=1 assuming a chi-square distribution).
After NONMEM modeling fitting, LLP can be executed using PsN with command like:
mod1.lst.-rplots=2 generates a few basic plots for output.-clean=0 keeps all NONMEM fitting records.-min_retries=3 usually needed to make sure each model fitting is successful.
Assumption: random difference in observations that leads to uncertainty in parameter estimates.
To obtain CI
After NONMEM modeling fitting, non-parametric bootstrap can be executed using PsN with command like:
-rplots=2 generates a few basic plots for output.Importance ratio (IR):
\[IR = \frac{e^{-0.5*dOFV}}{relPDF}\] \[dOFV = OFV_{i} - OFV_{final}\] \[relPDF = \frac{PDF_{i}}{PDF_{final}}\]
Rule of thumb:
m is large enough (500-1000): similar to 500-1000 refit in bootstrap.
M/m ratio is important for SIR validity (5:1 is a reasonable starting point).
After NONMEM modeling fitting, SIR can be executed using PsN with command like:
This will evaluate uncertainty of all model parameters based on 500 resampled parameter sets with a M/m ratio of 5:1 (2500:500).
-rplots=2 generates dOFV and a few other diagnostics.
What if the diagnostics is not satisfied?
If \(DF_{proposal}<DF_{reference}\), inflate proposal distribution variance.
sir -samples=2500 -resamples=500 -theta_inflation=1.5 -omega_inflation=1.5 -sigma_inflation=1.5 -rplots=2 mod1.ctlIf \(DF_{final}>DF_{reference}\), increase M/m ratio.
sir -samples=5000 -resamples=500 -rplots=2 mod1.ctlAfter NONMEM modeling fitting, multiple iteration SIR can be executed using PsN with command like:
-rplots=2 generates dOFV and a few other diagnostics.